Question

The length of the wire is doubled, Its conductance will

• A. remain unchanged
• B. be halved
• C. be doubled
• D. be quadrupled

Answer 1

Answer: (B)

be halved

Answer 2

Conductance is inverse of resistance. Conductance is given by $\sigma=\frac{1}{R}$ Substituting $R=\rho \frac{l}{A}$, we get $\sigma=\frac{A}{\rho l}$ If $A=$ constant, then we have $\sigma \propto \frac{1}{l} \Rightarrow \frac{\sigma_{2}}{\sigma_{1}}=\frac{l_{3}}{l_{2}}$ Substituting $l_{2}=2 l_{1}$, we get $\sigma_{2}=\frac{\sigma_{1}}{2}$ Therefore, conductance will be halved.